Description Usage Arguments Value Author(s) References Examples

Computes the pdf, cdf, value at risk and expected shortfall for the Ramber-Schmeiser distribution due to Ramberg and Schmeiser (1974) given by

*\begin{array}{ll}
&\displaystyle
{\rm VaR}_p (X) = \frac {p^b - (1 - p)^c}{d},
\\
&\displaystyle
{\rm ES}_p (X) = \frac {p^{b}}{d (b + 1)} + \frac {(1 - p)^{c + 1} - 1}{p d (c + 1)}
\end{array}*

for *0 < p < 1*, *b > 0*, the first shape parameter,
*c > 0*, the second shape parameter, and *d > 0*, the scale parameter.

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`p` |
scaler or vector of values at which the value at risk or expected shortfall needs to be computed |

`d` |
the value of the scale parameter, must be positive, the default is 1 |

`b` |
the value of the first shape parameter, must be positive, the default is 1 |

`c` |
the value of the second shape parameter, must be positive, the default is 1 |

`log` |
if TRUE then log(pdf) are returned |

`log.p` |
if TRUE then log(cdf) are returned and quantiles are computed for exp(p) |

`lower.tail` |
if FALSE then 1-cdf are returned and quantiles are computed for 1-p |

An object of the same length as `x`

, giving the pdf or cdf values computed at `x`

or an object of the same length as `p`

, giving the values at risk or expected shortfall computed at `p`

.

Saralees Nadarajah

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

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VaRES documentation built on May 29, 2017, 8:27 p.m.

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